Abstract

This paper investigates the millimeter electromagnetic waves passing through a metal nanogap. Based upon the study of a perfect electrical conductor model, we show that the electric field enhancement inside the gap saturates as the gap size approaches zero, and the ultimate enhancement strength is inversely proportional to the thickness of the metal film. In addition, no significant enhancement can be gained by decreasing the gap size further if the aspect ratio between the dimensions of the underlying geometric structure exceeds approximately 100.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).
  4. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
    [CrossRef]
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2013

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

2012

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

2010

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

B. Sturman, E. Podivilov, and M. Gorkunov, “Transmission and diffraction properties of a narrow slit in a perfect metal,” Phys. Rev. B 82, 115419 (2010).
[CrossRef]

2009

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9, 887–891 (2009).
[CrossRef] [PubMed]

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

2007

R. Gordon, “Angle-dependent optical transmission through a narrow slit in a thick metal film,” Phys. Rev. B 75, 193401 (2007).
[CrossRef]

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99, 137401 (2007).
[CrossRef] [PubMed]

2006

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef] [PubMed]

2005

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

2004

J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12, 6106–6121 (2004).
[CrossRef] [PubMed]

2002

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

2001

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 99, 5601–5603 (2001).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

1983

Ahn, J. S.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Ahn, K. J.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Alexander, R. W.

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bravo-Abad, J.

J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Brebbia, C. A.

C. A. Brebbia, Boundary Element Methods in Engineering (Springer, New York1982).
[CrossRef]

Chen, X.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Chilkoti, A.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Choi, S. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Ciraci, C.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Ebbesen, T. W.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Fernndez-Domnguez, A. I.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Gordon, R.

R. Gordon, “Angle-dependent optical transmission through a narrow slit in a thick metal film,” Phys. Rev. B 75, 193401 (2007).
[CrossRef]

Gorkunov, M.

B. Sturman, E. Podivilov, and M. Gorkunov, “Transmission and diffraction properties of a narrow slit in a perfect metal,” Phys. Rev. B 82, 115419 (2010).
[CrossRef]

Hill, R. T.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Im, H.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Jeoung, S. C.

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99, 137401 (2007).
[CrossRef] [PubMed]

Kang, D. H.

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99, 137401 (2007).
[CrossRef] [PubMed]

Kang, J. H.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Khim, K. S.

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99, 137401 (2007).
[CrossRef] [PubMed]

Kim, D. S.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99, 137401 (2007).
[CrossRef] [PubMed]

Kim, Y. J.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Koo, S. M.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Kuipers, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

Kurokawa, Y.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef] [PubMed]

Lee, J. W.

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99, 137401 (2007).
[CrossRef] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Lin, J.

J. Lin, H-M. Nguyen, and F. Reitich, “Electromagnetic field enhancement in small gaps: a rigorous mathematical theory,” preprint. http://www.auburn.edu/~jzl0097/publications.htm .

Lindquist, N. C.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Long, L. L.

Maier, S. A.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Mansuripur, M.

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
[CrossRef]

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Miyazaki, H. T.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef] [PubMed]

Mock, J. J.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Moloney, J. V.

Moreno, E.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

Nguyen, H-M.

J. Lin, H-M. Nguyen, and F. Reitich, “Electromagnetic field enhancement in small gaps: a rigorous mathematical theory,” preprint. http://www.auburn.edu/~jzl0097/publications.htm .

Nordlander, P.

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9, 887–891 (2009).
[CrossRef] [PubMed]

Oh, S. H.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Ordal, M. A.

Park, D. J.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Park, G. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Park, H. R.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Park, N.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Park, N. K.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Park, Q. H.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Pelton, M.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Pendry, J. B.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Piao, X.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Planken, P. C. M.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Podivilov, E.

B. Sturman, E. Podivilov, and M. Gorkunov, “Transmission and diffraction properties of a narrow slit in a perfect metal,” Phys. Rev. B 82, 115419 (2010).
[CrossRef]

Porto, J. A.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

Prodan, E.

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9, 887–891 (2009).
[CrossRef] [PubMed]

Reitich, F.

J. Lin, H-M. Nguyen, and F. Reitich, “Electromagnetic field enhancement in small gaps: a rigorous mathematical theory,” preprint. http://www.auburn.edu/~jzl0097/publications.htm .

Sambles, J. R.

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

Seo, M. A.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99, 137401 (2007).
[CrossRef] [PubMed]

Smith, D. R.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Sommerfeld, A.

A. Sommerfeld, Partial Differential Equations in Physics (Academic Press, New York1949).

Sturman, B.

B. Sturman, E. Podivilov, and M. Gorkunov, “Transmission and diffraction properties of a narrow slit in a perfect metal,” Phys. Rev. B 82, 115419 (2010).
[CrossRef]

Suwal, O. K.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Takakura, Y.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 99, 5601–5603 (2001).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Urzhumov, Y.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Ward, C. A.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Xie, Y.

Yang, F.

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

Zakharian, A. R.

Zuloaga, J.

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9, 887–891 (2009).
[CrossRef] [PubMed]

Appl. Opt.

Nano Lett.

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9, 887–891 (2009).
[CrossRef] [PubMed]

Nat. Commnun.

X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electro-magnetic waves,” Nat. Commnun. 4, 2361 (2013).

Nat. Photonics

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156, (2009).
[CrossRef]

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[CrossRef]

Opt. Express

Phys. Rev. B

R. Gordon, “Angle-dependent optical transmission through a narrow slit in a thick metal film,” Phys. Rev. B 75, 193401 (2007).
[CrossRef]

B. Sturman, E. Podivilov, and M. Gorkunov, “Transmission and diffraction properties of a narrow slit in a perfect metal,” Phys. Rev. B 82, 115419 (2010).
[CrossRef]

Phys. Rev. E

J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit,” Phys. Rev. E 69, 026601 (2004).
[CrossRef]

Phys. Rev. Lett.

Y. Takakura, “Optical resonance in a narrow slit in a thick metallic screen,” Phys. Rev. Lett. 99, 5601–5603 (2001).
[CrossRef]

F. Yang and J. R. Sambles, “Resonant transmission of microwaves through a narrow metallic slit,” Phys. Rev. Lett. 89, 063901 (2002).
[CrossRef] [PubMed]

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets,” Phys. Rev. Lett. 99, 137401 (2007).
[CrossRef] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys.

F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82, 729–787 (2010).
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Science

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernndez-Domnguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072 (2012).
[CrossRef] [PubMed]

Other

A. Sommerfeld, Partial Differential Equations in Physics (Academic Press, New York1949).

C. A. Brebbia, Boundary Element Methods in Engineering (Springer, New York1982).
[CrossRef]

J. Lin, H-M. Nguyen, and F. Reitich, “Electromagnetic field enhancement in small gaps: a rigorous mathematical theory,” preprint. http://www.auburn.edu/~jzl0097/publications.htm .

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Figures (8)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Electric field enhancement |E|/|Einc| inside and near the nano slit when the gap width W is 100 nm, 50 nm, and 10 nm, respectively.

Fig. 3
Fig. 3

(a). Magnetic field Hy inside and near the nano slit; (b). Hy in the middle of slit along the z direction (vertical dash line in (a)); (c). Hy on the cross-sectional lines of the slit (horizontal dash lines in (a)).

Fig. 4
Fig. 4

The induced current on the surface of metal films.

Fig. 5
Fig. 5

Magnetic field Hy along the boundaries of metal films for gap width W = 100 nm, 50 nm, 10 nm, 5 nm, 2 nm, and the magnetic field Hy,0 when no gap is present. Note the change of field near the gap apertures when the gap size decreases.

Fig. 6
Fig. 6

Magnetic field Hy in the middle of the slit along the z direction for gap width W = 100 nm, 50 nm, 10 nm, 5 nm and 2 nm, respectively. The black squares denote a−,0 and a+,0, the values of the magnetic field Hy,0 at z = 0 μm and z = 1 μm respectively in the absence of nano silt.

Fig. 7
Fig. 7

Enhancement factor Q for gap width W = 100 nm, 50 nm, 10 nm, 5 nm and 2 nm, respectively. The metal thickness T = 1 μm. Q saturates and approaches the limit Q 0 = | a + , 0 a , 0 | T k as the gap width decreases.

Fig. 8
Fig. 8

Enhancement factor Q for gap size W = 1μm, 500 nm, 100 nm, 50 nm, and 10 nm, respectively. The metal thickness T = 10 μm. Square: calculation based on the PEC model; circle: calculation with the Drude model for real metals.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

2 H y x 2 + 2 H y z 2 + k 2 H y = 0 .
H y n = 0 on the metal boundaries .
Q = slit region | E | d x d z slit region | E inc | d x d z .
Q = 1 A slit region | E | | E inc | d x d z ,
H y ( x , z ) = n = 0 ( α n e i γ n z + β n e i γ n ( z T ) ) cos ( n π x W ) ,
B 1 sin ( k z + ϕ 1 ) + i B 2 sin ( k z + ϕ 2 ) .
sin ( k z + ϕ i ) = sin ϕ i + 2 π cos ϕ i ( z / λ ) + O ( z 2 / λ 2 ) , i = 1 , 2 .
H y ( x , z ) = a z + b for δ z T δ ,
E = ( E x , 0 , 0 ) δ z T δ ,
| E | | E inc | = | a | k , δ z T δ .
Q | a + , W a , W | T k ,
Q 0 = | a + , 0 a , 0 | T k
ε ( ω ) = 1 w p 2 ω ( ω + i γ ) .

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